Here n is a positive integer, and you may use the standard formulas for Σ k, Σ k² and Σ k³. Which of the following statements are true?

MathematicsAdvancedHigh School (11–12)Algebra › Sequences and Series JEE Advanced

Here $n$ is a positive integer, and you may use the standard formulas for $\sum k$ , $\sum k^2$ and $\sum k^3$ . Which of the following statements are true?

One or more options are correct. Tick all the correct ones: a wrong option costs marks, and a part-right answer earns part of the marks.

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← For every positive integer n, the sum of the first n terms of a sequence is Sn = 3 · 2ⁿ + n² - 3. What is the 10th term of the sequence? (The sequence is neither an arithmetic nor a geometric progression.)The nonzero real numbers a, b and c are three consecutive terms of a geometric progression with common ratio r, and a, 2b and 3c are three consecutive terms of an arithmetic progression. Which of the following statements are true? →

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